1. Field of the Invention
The present invention relates generally to control systems and, more particularly, to a system and method for reducing effects of unmodeled dynamics in real-world systems subject to control.
2. Prior Art
Real-world dynamic systems often exhibit resonance properties, which are associated with high-order dynamics that are unnecessary and undesirable for proper operation. The high-order effects are imposed on the dominant dynamics of the system which is, in contrast, essential to achieve required functionality. Typical examples are mechanical systems, such as rotating machinery, machine tools, robotic manipulators and space structures, which frequently exhibit numerous resonance conditions associated with inevitable elasticity of mechanical components. In many practical situations, the higher-order dynamics are difficult to identify and remain excluded from the theoretical model of the system.
When feedback control is applied to enhance operation of a dynamic system, the presence of the higher-order dynamics results in undesirable oscillations, affects overall stability, and leads to limited control performance. Considering the level of contribution of high-order dynamics to the output of a dynamic system, the following two categories of control applications can be identified:
In the first category, the effects of the high-order dynamics under given operating conditions exceed acceptable errors in the output of the system. Typical examples are found in light robotic manipulators and space structures where excessive deflections of structural members and links directly affect positioning accuracy. The deflections may result from external excitation or internal actuation, such as execution of commanded trajectory profiles in the case of robotic manipulators. Since the presence of the high-order dynamics leads to unacceptable errors in the output, the control system needs to be selected and designed to take account and to suppress the higher-order dynamic effects. Prior art strategies in this area include the following categories of control methods: feedback of state variables which represent the high-order dynamics of the system subject to control; input shaping methods suitable for open-loop and closed-loop implementation; boundary control techniques for mechanical systems; and passive, semi-active and active vibration damping strategies for mechanical systems.
The second category comprises dynamic systems where the effects of the high-order dynamics on the output subject to control remain within acceptable limits and, therefore, can be tolerated without sacrificing desired accuracy. In this case, however, the high-order dynamics may degrade overall stability and become a limiting factor for the control performance. These difficulties frequently arise when the bandwidth required for proper operation approaches the lowest resonance frequency of the controlled system and/or there is not enough inherent damping to prevent instability. The bandwidth of a system is defined to be the maximum frequency at which the output of a system will track an input sinusoid in a satisfactory manner. By convention, for linear systems with non-zero DC gain, the bandwidth is the frequency of the input at which the output is attenuated to a factor of 0.707 times the input (or down 3 dB) relative to the DC gain. Typical example applications in this category include industrial robots and precision machine tools. Despite the rugged design that prevents structural deflections beyond required accuracy, the high-performance servo controllers for these applications have to cope with numerous lightly-damped resonance conditions. In general, the control methods listed above for the first category can be considered as potential solutions. However, their practical use is limited due to one or more of the following requirements and complications: a complete and accurate model of the controlled system is necessary, additional sensing and/or actuation arrangements are required, computational and/or hardware complexity increases undesirably, or the level of sensitivity to variations in the system parameters is not acceptable. Since the presence of the higher-order dynamics does not affect accuracy of the output beyond acceptable limits, direct suppression of the higher-order dynamic effects on the output of the system is not critical. Consequently, simpler methods, such as implementation of low-pass filters and band-reject filters, are preferably adopted in practice to improve stability and to enhance control performance. However, the effectiveness of these approaches is limited since low-pass filters generally introduce amplitude distortion and destabilizing phase lag, and band-reject filters are not suitable for applications where the resonance conditions shift during operation, change due to regular wear and tear, or vary because of production inconsistency.
In a first aspect, the present invention is directed to a system for extracting a signal component that represents dominant dynamics of a dynamic system from an output signal of a dynamic system. In one embodiment, the system comprises a state observer and a corrector filter. The state observer is adapted to track a signal component that represents the dominant dynamics in the output signal of the dynamic system, and provide an estimation signal representing an estimated signal component that represents the dominant dynamics in the output signal of the dynamic system. The corrector filter is adapted to compensate for a mismatch between the estimation signal and the actual signal component that represents the dominant dynamics in the output signal. A combination of the estimation signal with an output signal of the corrector filter can provide a synthesized signal including the signal component that represents the dominant dynamics in the output signal of the dynamic system.
In another aspect, the present invention is directed to a method of extracting a signal component that represents dominant dynamics of a dynamic system from an output signal of a dynamic system. In one embodiment, the method comprises estimating a signal component that represents the dominant dynamics in the dynamic system output signal and compensating for a mismatch between the estimated signal component and an actual signal component that represents the dominant dynamics in the dynamic system output signal. The estimated signal component can be combined with a signal representing the compensation for a mismatch between the estimated signal component and the actual signal component to provide a synthesized signal including the signal component that represents the dominant dynamics in the output signal.
In a further aspect, the present invention is directed to a method of reducing destabilizing effects of high-order dynamics in a controlled system. In one embodiment, the method comprises tracking a signal component that represents dominant dynamics in an output signal of the controlled system and providing an estimation signal representing an estimated component that represents the dominant dynamics in the output signal of the controlled system. A mismatch between the estimation signal and the actual signal component that represents the dominant dynamics is compensated for by combining the estimation signal and an output signal from a corrector filter to form a synthesized feedback signal. The synthesized feedback signal includes a signal component that represents the dominant dynamics in the output signal of the controlled system and is inputted to a controller for the controlled system, wherein a destabilizing effect of unmodeled higher order dynamic signal components in the dynamic system output signal is reduced or substantially eliminated.